Compositional Game Theory, compositionally

Atkey, Robert and Gavranović, Bruno and Ghani, Neil and Kupke, Clemens and Ledent, Jérémy and Nordvall Forsberg, Fredrik (2020) Compositional Game Theory, compositionally. In: Applied Category Theory 2020, 2020-07-06 - 2020-07-10.

[img]
Preview
 Text (Atkey-etal-ACT2020-Compositional-Game-Theory-compositionally)
Atkey_etal_ACT2020_Compositional_Game_Theory_compositionally.pdf
Accepted Author Manuscript
License: Creative Commons Public Domain (CC0)
Download (304kB)| Preview

    Abstract

    We present a new compositional approach to compositional game theory (CGT) based upon Arrows, a concept originally from functional programming, closely related to Tambara modules, and operators to build new Arrows from old. We model equilibria as a module over an Arrow and define an operator to build a new Arrow from such a module over an existing Arrow. We also model strategies as graded Arrows and define an operator which builds a new Arrow by taking the colimit of a graded Arrow. A final operator builds a graded Arrow from a graded bimodule. We use this compositional approach to CGT to show how known and previously unknown variants of open games can be proven to form symmetric monoidal categories.

    Creators(s): Atkey, Robert ORCID logoORCID: https://orcid.org/0000-0002-4414-5047, Gavranović, Bruno, Ghani, Neil ORCID logoORCID: https://orcid.org/0000-0002-3988-2560, Kupke, Clemens, Ledent, Jérémy ORCID logoORCID: https://orcid.org/0000-0001-7375-4725 and Nordvall Forsberg, Fredrik ORCID logoORCID: https://orcid.org/0000-0001-6157-9288;
    Item type:Conference or Workshop Item(Paper)
    ID code:73674
    Keywords:compositional game theory (CGT), equilibria, Arrow, compositional approach, Electronic computers. Computer science, Computer Science(all)
    Subjects:Science > Mathematics > Electronic computers. Computer science
    Department:Faculty of Science > Computer and Information Sciences
    Depositing user: Pure Administrator
    Date deposited:20 Aug 2020 14:20
    Last modified:21 Dec 2020 02:49
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/73674
    Export data:
    CORE (COnnecting REpositories)